<s>
Computer-generated	B-Algorithm
holography	I-Algorithm
(	O
CGH	O
)	O
is	O
the	O
method	O
of	O
digitally	O
generating	O
holographic	B-Algorithm
interference	O
patterns	O
.	O
</s>
<s>
A	O
holographic	B-Algorithm
image	I-Algorithm
can	O
be	O
generated	O
e.g.	O
</s>
<s>
by	O
digitally	O
computing	O
a	O
holographic	B-Algorithm
interference	O
pattern	O
and	O
printing	O
it	O
onto	O
a	O
mask	O
or	O
film	O
for	O
subsequent	O
illumination	O
by	O
suitable	O
coherent	O
light	O
source	O
.	O
</s>
<s>
Alternatively	O
,	O
the	O
holographic	B-Algorithm
image	I-Algorithm
can	O
be	O
brought	O
to	O
life	O
by	O
a	O
holographic	B-Algorithm
3D	B-Algorithm
display	I-Algorithm
(	O
a	O
display	O
which	O
operates	O
on	O
the	O
basis	O
of	O
interference	O
of	O
coherent	O
light	O
)	O
,	O
bypassing	O
the	O
need	O
of	O
having	O
to	O
fabricate	O
a	O
"	O
hardcopy	O
"	O
of	O
the	O
holographic	B-Algorithm
interference	O
pattern	O
each	O
time	O
.	O
</s>
<s>
Consequently	O
,	O
in	O
recent	O
times	O
the	O
term	O
"	O
computer-generated	B-Algorithm
holography	I-Algorithm
"	O
is	O
increasingly	O
being	O
used	O
to	O
denote	O
the	O
whole	O
process	O
chain	O
of	O
synthetically	O
preparing	O
holographic	B-Algorithm
light	O
wavefronts	O
suitable	O
for	O
observation	O
.	O
</s>
<s>
Computer-generated	B-Algorithm
holograms	I-Algorithm
have	O
the	O
advantage	O
that	O
the	O
objects	O
which	O
one	O
wants	O
to	O
show	O
do	O
not	O
have	O
to	O
possess	O
any	O
physical	O
reality	O
at	O
all	O
(	O
completely	O
synthetic	O
hologram	B-Algorithm
generation	O
)	O
.	O
</s>
<s>
On	O
the	O
other	O
hand	O
,	O
if	O
holographic	B-Algorithm
data	O
of	O
existing	O
objects	O
is	O
generated	O
optically	O
,	O
but	O
digitally	O
recorded	O
and	O
processed	O
,	O
and	O
brought	O
to	O
display	O
subsequently	O
,	O
this	O
is	O
termed	O
CGH	O
as	O
well	O
.	O
</s>
<s>
Ultimately	O
,	O
computer-generated	B-Algorithm
holography	I-Algorithm
might	O
serve	O
all	O
the	O
roles	O
of	O
current	O
computer-generated	O
imagery	O
:	O
holographic	B-Algorithm
computer	O
displays	O
for	O
a	O
wide	O
range	O
of	O
applications	O
from	O
CAD	B-Application
to	O
gaming	O
,	O
holographic	B-Algorithm
video	O
and	O
TV	O
programs	O
,	O
automotive	O
and	O
communication	O
applications	O
(	O
cell	O
phone	O
displays	O
)	O
and	O
many	O
more	O
.	O
</s>
<s>
Holography	B-Algorithm
is	O
a	O
technique	O
originally	O
invented	O
by	O
Hungarian	O
physicist	O
Dennis	O
Gabor	O
(	O
1900	O
–	O
1979	O
)	O
to	O
improve	O
the	O
resolving	O
power	O
on	O
electron	O
microscopes	O
.	O
</s>
<s>
Reconstruction	O
:	O
Modulating	O
the	O
interference	O
pattern	O
onto	O
a	O
coherent	O
light	O
beam	O
by	O
technological	O
means	O
,	O
to	O
transport	O
it	O
to	O
the	O
user	O
observing	O
the	O
hologram	B-Algorithm
.	O
</s>
<s>
Computer	B-Algorithm
generated	I-Algorithm
holograms	I-Algorithm
offer	O
important	O
advantages	O
over	O
the	O
optical	O
holograms	B-Algorithm
since	O
there	O
is	O
no	O
need	O
for	O
a	O
real	O
object	O
.	O
</s>
<s>
Because	O
of	O
this	O
breakthrough	O
,	O
a	O
three-dimensional	B-Algorithm
display	I-Algorithm
was	O
expected	O
when	O
the	O
first	O
algorithms	O
were	O
reported	O
at	O
1966	O
.	O
</s>
<s>
were	O
proposed	O
in	O
the	O
fields	O
of	O
holographic	B-Algorithm
information	O
and	O
computational	O
reduction	O
as	O
well	O
as	O
in	O
computational	O
and	O
quantization	O
techniques	O
.	O
</s>
<s>
In	O
the	O
first	O
one	O
,	O
the	O
Fourier	B-Algorithm
transformation	I-Algorithm
is	O
used	O
to	O
simulate	O
the	O
propagation	O
of	O
each	O
plane	O
of	O
depth	O
of	O
the	O
object	O
to	O
the	O
hologram	B-Algorithm
plane	O
.	O
</s>
<s>
The	O
Fourier	B-Algorithm
transformation	I-Algorithm
concept	O
was	O
first	O
introduced	O
by	O
Brown	O
and	O
Lohmann	O
with	O
the	O
detour	O
phase	O
method	O
leading	O
to	O
cell	O
oriented	O
holograms	B-Algorithm
.	O
</s>
<s>
replaced	O
the	O
cell	O
oriented	O
holograms	B-Algorithm
by	O
point	O
holograms	B-Algorithm
and	O
made	O
this	O
kind	O
of	O
computer	B-Algorithm
generated	I-Algorithm
holograms	I-Algorithm
more	O
attractive	O
.	O
</s>
<s>
In	O
a	O
Fourier	B-Algorithm
Transform	I-Algorithm
hologram	B-Algorithm
the	O
reconstruction	O
of	O
the	O
image	O
occurs	O
in	O
the	O
far	B-Algorithm
field	I-Algorithm
.	O
</s>
<s>
These	O
holograms	B-Algorithm
are	O
called	O
Fourier	O
Based	O
Holograms	B-Algorithm
.	O
</s>
<s>
First	O
CGHs	O
based	O
on	O
the	O
Fourier	B-Algorithm
transform	I-Algorithm
could	O
reconstruct	O
only	O
2D	O
images	O
.	O
</s>
<s>
Brown	O
and	O
Lohmann	O
introduced	O
a	O
technique	O
to	O
calculate	O
computer	B-Algorithm
generated	I-Algorithm
holograms	I-Algorithm
of	O
3D	O
objects	O
.	O
</s>
<s>
The	O
wavefront	O
to	O
be	O
reconstructed	O
by	O
the	O
hologram	B-Algorithm
is	O
,	O
therefore	O
,	O
the	O
superposition	O
of	O
the	O
Fourier	B-Algorithm
transforms	I-Algorithm
of	O
each	O
object	O
plane	O
in	O
depth	O
,	O
modified	O
by	O
a	O
quadratic	O
phase	O
factor	O
.	O
</s>
<s>
An	O
elementary	O
hologram	B-Algorithm
is	O
calculated	O
for	O
every	O
point	O
source	O
and	O
the	O
final	O
hologram	B-Algorithm
is	O
synthesized	O
by	O
superimposing	O
all	O
the	O
elementary	O
holograms	B-Algorithm
.	O
</s>
<s>
This	O
concept	O
has	O
been	O
first	O
reported	O
by	O
Waters	O
whose	O
major	O
assumption	O
originated	O
with	O
Rogers	O
who	O
recognized	O
that	O
a	O
Fresnel	O
zone	O
plate	O
could	O
be	O
considered	O
a	O
special	O
case	O
of	O
the	O
hologram	B-Algorithm
proposed	O
by	O
Gabor	O
.	O
</s>
<s>
But	O
,	O
as	O
far	O
as	O
most	O
of	O
the	O
object	O
points	O
were	O
non-zero	O
,	O
the	O
computational	O
complexity	O
of	O
the	O
point-source	O
concept	O
was	O
much	O
higher	O
than	O
in	O
the	O
Fourier	B-Algorithm
transformation	I-Algorithm
concept	O
.	O
</s>
<s>
Some	O
researchers	O
tried	O
to	O
overcome	O
this	O
drawback	O
by	O
predefining	O
and	O
storing	O
all	O
the	O
possible	O
elementary	O
holograms	B-Algorithm
using	O
special	O
data	O
storage	O
techniques	O
because	O
of	O
the	O
huge	O
capacity	O
that	O
is	O
needed	O
in	O
this	O
case	O
,	O
others	O
by	O
using	O
special	O
hardware	O
.	O
</s>
<s>
Ray	O
tracing	O
is	O
perhaps	O
the	O
simplest	O
method	O
of	O
computer	B-Algorithm
generated	I-Algorithm
holography	I-Algorithm
to	O
visualize	O
.	O
</s>
<s>
However	O
,	O
some	O
technical	O
restraints	O
,	O
like	O
computation	O
and	O
storage	O
capacity	O
,	O
still	O
burden	O
digital	O
holography	B-Algorithm
which	O
makes	O
real-time	O
applications	O
almost	O
impossible	O
with	O
current	O
standard	O
computer	O
hardware	O
.	O
</s>
<s>
Early	O
forms	O
of	O
pure	O
amplitude	O
holograms	B-Algorithm
were	O
simply	O
printed	O
in	O
black	O
and	O
white	O
,	O
meaning	O
that	O
the	O
amplitude	O
had	O
to	O
be	O
encoded	O
with	O
one	O
bit	O
of	O
depth	O
only	O
.	O
</s>
<s>
One	O
is	O
based	O
on	O
phase-only	O
or	O
amplitude-only	O
modulation	O
and	O
consecutive	O
spatial	O
filtering	O
,	O
the	O
other	O
one	O
is	O
based	O
on	O
polarization	O
holograms	B-Algorithm
with	O
variable	O
orientation	O
and	O
magnitude	O
of	O
local	O
birefringence	O
.	O
</s>
<s>
Holographic	B-Algorithm
displays	O
are	O
currently	O
yet	O
a	O
challenge	O
(	O
)	O
,	O
although	O
successful	O
prototypes	O
have	O
been	O
built	O
.	O
</s>
<s>
An	O
ideal	O
display	O
for	O
computer	B-Algorithm
generated	I-Algorithm
holograms	I-Algorithm
would	O
consist	O
of	O
pixels	O
smaller	O
than	O
a	O
wavelength	O
of	O
light	O
with	O
adjustable	O
phase	O
and	O
brightness	O
.	O
</s>
<s>
Recently	O
computer-generated	B-Algorithm
holography	I-Algorithm
has	O
been	O
extended	O
in	O
its	O
usage	O
beyond	O
light	O
optics	O
,	O
and	O
applied	O
in	O
generating	O
structured	O
electron	O
wavefunctions	O
with	O
a	O
desired	O
amplitude	O
and	O
phase	O
profile	O
.	O
</s>
<s>
The	O
computer	B-Algorithm
generated	I-Algorithm
holograms	I-Algorithm
are	O
designed	O
by	O
the	O
interference	O
of	O
a	O
target	O
wave	O
with	O
a	O
reference	O
wave	O
,	O
which	O
could	O
be	O
,	O
e.g.	O
</s>
<s>
The	O
holographic	B-Algorithm
diffractive	O
optical	O
elements	O
used	O
are	O
usually	O
constructed	O
out	O
of	O
thin	O
membranes	O
of	O
materials	O
such	O
as	O
silicon	O
nitride	O
.	O
</s>
